Blender Guru Tutorial - Part 5 - Coffee Cup
You have Proportional Editing on with Random Falloff selected. You can turn this off by pressing O once or twice or by changing the menu manually at the bottom of the 3D Viewport.

A Gif to explain:



Proportional Editing can be extremely useful for deforming a mesh in a mathematically precise way. For example, with your coffee cup, I might loop cut the main cylinder several times and then use proportional editing with Smooth Falloff while scaling the bottom loop to create a loose conic shape. I then might use Sphere Falloff to widen the middle and shrink the top.